Fast Radon Transform and Velocity Analysis Applications

Abstract

A powerful and fast algorithm is proposed to perform a Radon Transform to be used in 3-D seismic problems when the subsurface geometry is 1-D. A point source recording is then decomposed into planes waves, which gives a simpler structure to seismograms.

The Radon Transform, as well as the inverse Radon Transform, can be decomposed into subsequent Fourier Transform, Hankel Transform and Inverse Fourier Transform. An original multiple vectorized Fast Hankel Transform is coupled with multiple vectorized FFT transforms and provides an algorithm with a high performance level. For instance, the Fast Radon Transform applied to a 5 seconds long point source recording composed of 216 traces requires an average of 4 seconds CPU time on a one processor Cray XMP.

Among the numerous applications of the slant stack procedure, a velocity analysis is proposed which displays the following property: the reflections from a stratified subsurface appear, in the (τ, p) domain, on curves which are built with ellipses equations. A coherency analysis, whose objective is to transform the ellipses into straight lines, pilots a velocity analysis offering more accuracy than the well-known Dix formula.

Various results are given upon Radon transforms and velocity analysis performed successfully on synthetic and field data.